The benchmark Nikkei 225 jumped 598.49 points, or 3.68 percent, to 16,874.44, retracing its 3.4 percent loss in the previous session. Japanese stocks were boosted by a relatively weaker yen against the dollar and as market players digested the extent of damage from last week's earthquakes.

Australia's ASX 200 added 51.74 points, or 1.01 percent, to 5,188.80, with the energy and materials subindexes leading gains. In South Korea, the Kospi closed up 2.26 points, or 0.11 percent, at 2,011.36.

Hong Kong's Hang Seng index was up 0.76 percent as of 3:14 p.m. HK/SIN time. Chinese mainland markets also advanced, with the Shanghai composite closing up 9.28 points, or 0.31 percent, at 3,042.94, and the Shenzhen composite adding 5.79 points, or 0.29 percent, at 1,958.20.

Oil advanced during Asian hours, after paring most of its losses overnight. Global benchmark Brent added 0.56 percent to $43.15 a barrel as of 2:42 p.m. HK/SIN time, after settling down 0.4 percent. U.S. crude futures were up 0.78 percent at $40.09 a barrel, after finishing down 1.4 percent overnight.

Toshifumi Kitamura | AFP | Getty Images

Pedestrians walk in front of an electronic stock indicator at the window of a security company in Tokyo on Monday, April 18, 2016. The Japanese benchmark Nikkei 225 sold off sharply, falling over 3 percent during the session.

On Sunday, the world's largest oil exporting countries failed to reach an agreement in Doha, Qatar, to freeze output at January levels in order to tackle the global supply glut.

The deal's failure initially sent oil prices tumbling over 5 percent on Monday. The reversal came after reports said that a workers' strike in Kuwait had hit the gulf country's daily oil output. Reuters reported that the strike cut the OPEC producer's crude output by more than 60 percent, from about 3 million barrels per day to about 1.1 million.

Analysts said Kuwait's reduction in output remains supportive for crude for the time being.

The reversal in oil prices gave an overnight boost to commodity currencies such as the Australian dollar.

The Aussie traded at $0.7793 as of 2:45 p.m. HK/SIN time, compared with around $0.76 during Asian hours in the previous session.

"Investors were relieved that oil did not fall 10 percent on the back of the Doha meeting and they were quick to reward risk currencies like the Australian and New Zealand dollars with gains," said Kathy Lien, managing director of foreign exchange strategy at BK Asset Management, in a morning note.

In the minutes of its most recent meeting, released Tuesday, the Reserve Bank of Australia said it was concerned about the impact of a rising Australian dollar, noting "an appreciating exchange rate could complicate progress in activity rebalancing towards the non-mining sectors of the economy." The RBA also noted that low inflation could allow it to cut interest rates further. At the April 5 meeting, the RBA had kept rates steady at a record low 2.0 percent.

Goldman Sachs analysts said in a note that the minutes did not provide a strong signal for a near term rate cut, but they added that it is too early to rule out a potential cut in May altogether, "given the upward pressure on the Aussie dollar and related downward risks to growth and inflation."

The Japanese yen, which touched levels under 108 against the dollar in the previous session, advanced late in the session. As of 2:50 p.m. HK/SIN time, after the Japan market close, the dollar/yen pair traded at 108.77, after reaching as high as 109.20 earlier.

Major Japanese exporters saw a rebound in their stock prices, with automakers Toyota, Nissan and Honda adding between 3.57 and 4.46 percent. Shares of Sony rebounded 6.49 percent. Shares of exporters, which typically benefit from a weaker yen, had tumbled in the previous session after reports said some manufacturers were affected by the earthquakes that struck Kyushu island in the south of Japan last week, causing sizable damage.

Reuters reported that Sony and Honda have said their affected production plants in the region will remain suspended for the time being.

In a media statement on Sunday, Toyota said it would suspend production on its vehicle assembly lines in stages, between April 18 and April 23, due to supply shortages resulting from the quakes.

Analysts didn't expect broader damage to Japan's economy.

Marcel Thieliant, a senior Japan economist at Capital Economics, said in a morning note, "the scale of damage does not appear huge and production shutdowns by major manufacturers should be reversed before long."

But Thieliant added that in the short term, the impact of the disaster would also be felt outside of the Kumamoto prefecture. In particular, he said the "shutdown at Toyota could reduce industrial output by up to 1.8 percent in April," adding the impact will be larger if the shutdown persisted for longer.

In South Korea, the central bank kept its base rate unchanged at 1.5 percent, in line with a Reuters poll. In a statement on its website, the Bank of Korea said it forecast the domestic economy will show "a trend of modest improvement going forward," centering around domestic demand activities.

The Korean Won strengthened against the dollar, with the pair trading down 0.83 percent at 1,133.94 as of 3:25 p.m. HK/SIN time, compared with the previous session's close at 1,143.38.

In company news, shares of Seven & i Holdings in Japan closed up 1.2 percent, as the company undergoes a leadership shuffle. According to the Nikkei, Seven & i's board is likely to approve a new management team Tuesday.

The Nikkei reported today that on April 7, the board had rejected a proposal, pushed by group chairman and CEO Toshifumi Suzuki, which included removing the president of Seven-Eleven Japan, Ryuichi Isaka. Suzuki has since announced his resignation from all positions in the group, according to the Nikkei.

Down Under, major miner Rio Tinto cut its 2017 production guidance from its Australian iron ore mines due to a delay in its AutoHaul system - a fully-autonomous heavy haul, long distance railway system. In a statement to the ASX, Rio Tinto said production from its Pilbara operations is now expected to be between 330 and 340 million tonnes in 2017, compared with a previous guidance of 350 million tonnes.